General Technological Background of the Invention
When signals, particularly but not always electromagnetic signals, are used in technological applications, the signal is received at a receiver as a time dependent signal and characteristics of the signal carry information that will often represent a physical quantity. The characteristics of the signal that are used to carry the information may be, for example, the magnitude of the signal at a time instant, or the phase of the signal, or the magnitude of a frequency component of the signal. In using the phase of a signal to carry information, the differential phase of the signal may be used for the sake of efficiency.
After the signal is received at a receiver it is processed. The processing of the signal may be carried out in hardware specifically designed for the purpose, or it may be carried out in a general purpose computer that has been programmed for that particular purpose.
Within the processing hardware, or the general purpose computer, the received signal is processed in the form of a time series of electric signals, which may be either analog (continuous data) or digital (discontinuous data). The received signal will be represented during processing by numerical values that correspond to physical characteristics of the signal, which in turn will have physical significance in the outside world. For example, a received signal may be an electromagnetic signal that represents a person's voice and that is being transmitted by radio. The received signal may be processed first, for example to remove interference effects, and then reconstituted and applied to a loudspeaker and converted into sound waves. Or the received signal may be a seismic signal, representative of an earthquake at some remote location, which is processed as analog or digital data and then displayed in a seismograph.
The processing of the signal may be represented by mathematical models. The models include transforms that operate on the data values of the signal being processed to produce a new set of transformed data values, which in turn represent a physical characteristic of the signal. The transformed signal may then be used in a variety of applications. One extremely well known transformation is the Fourier transform, which essentially resolves a time based signal into its frequency components. Knowledge of the frequency components of an electromagnetic signal can be useful in an enormous range of applications, including analysis of seismic waves, radio transmission and data compression.
The invention described in this patent documents relates in one aspect of the invention to the transformation of a signal into a transformed signal that is specified by the fades of the signal. The received signal will be described by the notation m(t), indicating that the signal is time dependent, and the transformed signal will be described by the notation M(f). These are conventional notations, and it will be appreciated that the parameter t can be replaced by any other suitable parameter having similar ordering properties. In order to calculate the locations and depths of the fades, the signal is first acquired and the low pass equivalent of the input signal is generated to expose the fades.
Where the envelope of the low pass equivalent signal m(t) is below some pre-determined threshold, such as a given number of decibels, for example 15 dB, below the running mean of the envelope of the signal, is referred to in this patent document as a fade of the signal m(t). this patent document, m(t) is compressed into a new signal characterized, in one aspect of the invention, by the locations of fades of the signal, and in another aspect also by the depths of the fades of the signal.
The fades of the signal m(t) correspond to z-domain (complex) zeros of the signal. In general, the zeros (real and complex) of a BL (band limited) function m(t) can be regarded as characteristics with a significance similar to that of the Nyquist samples or of the Fourier series coefficients of m(t). The purely real zeros of a real function correspond to the conventional zero axis crossing and therefore can be easily extracted through a simple zero crossing procedure. A complete discussion of the use of real zeros can be found in U.S. Pat. No. 3,510,640 to Voelker and the references found therein. By contrast, the z-domain zeros are the zeros of the function in the complex plane, and represent local minimums of the envelope of the function.
The z-domain zeros may be used to estimate the discrete spectrum of m(t), and the differential phase of m(t) may be derived from the envelope of m(t) using the concept of the z-domain zeros. Also, speech may be compressed based on the z-domain zeros of a signal m(t) that represents a speech signal, and knowledge of the location of fades may be used in interference reduction at single moving antennas.